# Lesson 3

Balanced Moves

Let's rewrite equations while keeping the same solutions.

### Problem 1

In this hanger, the weight of the triangle is $$x$$ and the weight of the square is $$y$$.

1. Write an equation using $$x$$ and $$y$$ to represent the hanger.

2. If $$x$$ is 6, what is $$y$$?

### Problem 2

Andre and Diego were each trying to solve $$2x+6=3x-8$$. Describe the first step they each make to the equation.

1. The result of Andre’s first step was $$\text-x+6=\text-8$$.

2. The result of Diego’s first step was $$6=x-8$$.

### Problem 3

1. Complete the table with values for $$x$$ or $$y$$ that make this equation true: $$3x+y=15$$.

 $$x$$ $$y$$ 2 6 0 3 3 0 8

2. Create a graph, plot these points, and find the slope of the line that goes through them.​​​​

(From Unit 3, Lesson 11.)

### Problem 4

Match each set of equations with the move that turned the first equation into the second.

### Problem 5

Select all the situations for which only zero or positive solutions make sense.

A:

Measuring temperature in degrees Celsius at an Arctic outpost each day in January.

B:

The height of a candle as it burns over an hour.

C:

The elevation above sea level of a hiker descending into a canyon.

D:

The number of students remaining in school after 6:00 p.m.

E:

A bank account balance over a year.

F:

The temperature in degrees Fahrenheit of an oven used on a hot summer day.

(From Unit 3, Lesson 14.)